An implementation of a discretization method for semi-infinite programming
Mathematical Programming: Series A and B
A note on an implementation of a method for quadratic semi-infinite programming
Mathematical Programming: Series A and B
Linear optimization and extensions: theory and algorithms
Linear optimization and extensions: theory and algorithms
SIAM Review
A mathematical view of interior-point methods in convex optimization
A mathematical view of interior-point methods in convex optimization
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Semi-definite programs are convex optimization problems arising in a wide variety of applications and the extension of linear programming. Most methods for linear programming have been generalized to semi-definite programs. This paper discusses the discretization method in semi-definite programming. The convergence and the convergent rate of error between the optimal value of the semi-definite programming problems and the optimal value of the discretized problems are obtained. An approximately optimal division is given under certain assumptions. With the significance of the convergence property, the duality result in semi-definite programs is proved in a simple way which is different from the other common proofs.